​​The application of pressure to quantum materials often induces transitions to new and sometimes unexpected states of matter. It is also a common way to get an insight into the physical properties of these materials by monitoring their response to a change of a well-controlled parameter. In the case of strongly correlated electron systems, dramatic effects are often observed at moderate pressure, enabling the use of a rather large panel of probes for their experimental investigation.

Here we are interested in manganese silicide (MnSi). This intermetallic compound is known for its uncommon, so-called helical magnetic order (i.e. the magnetic moments order spatially in the form of a spiral) and it is recognised as a paradigm of weak itinerant magnetism*. It is also the compound in which the first lattice of magnetic skyrmions has been evidenced in 2009 [1] in response to the application of a modest magnetic field. Skyrmions are a kind of “spin vortex” that emerges from the helical order in a limited region of the temperature-magnetic field phase diagram. They are a robust topological structure that can be manipulated as a whole. Hence, they have potential applications in spintronics. Moreover, when MnSi is submitted to hydrostatic pressure, the helical magnetic order together with the skyrmions is rapidly suppressed with a transition temperature vanishing at a low critical pressure p_c ≈ 1.5 GPa.

A major issue for this model system, like in most strongly correlated quantum materials, is to determine precisely the minimum effective microscopic Hamiltonian suitable for a description of its physical properties: in the case of MnSi, the magnetic ordering temperature and the parameters driving the appearance of the skyrmions. In the letter published in PRL [2], an international collaboration driven by researchers from PHELIQS/IMAPEC (UGA, CEA, Grenoble INP) could determine the amplitude and the pressure (p) dependence of the exchange constant J, which is the main parameter controlling the magnetism of MnSi. It is one of the very rare determinations of J(p) in a quantum material.

This is achieved through zero-field muon spin rotation measurements performed in PSI (Paul Scherrer Institute, Villigen, Switzerland) using a single crystal grown in PHELIQS/IMAPEC laboratory. With this technique, we determine the temperature dependence m(T) of the magnetic moment m at different pressures. It follows a quadratic dependence with temperature, i.e. m(T) = m(T=0) (1 − a T²), that is the signature of spin waves excitations with a dispersion relation law pertaining to a helical magnetic order. The exchange constant J which derives from parameter a is plotted as a function of p in Fig. 1.

This parameter is found to rapidly decrease with p and to follow the relation J ~ T_c/m²(T=0) that can be deduced from standard theory. From this law and the pressure dependence of both T_c and m(T=0) on the approach of p_c, we conclude that the suppression of the magnetic order arises from the cancellation of J, rather than from other origins such as, e.g. a quantum-fluctuation induced reduction of m. Our result suggests that the suppression of magnetic order under pressure in other metallic systems of the same family, e.g. FeGe or MnGe, proceeds from a similar mechanism. ​Finally, it provides a benchmark for ab-initio theories which endeavour to reproduce several key physical parameters of this series of strongly correlated systems.

​Itinerant magnets* are a class of metallic systems in which the ordered magnetic moment is coming from a polarization of the conduction bands, not from localized ions. A hallmark of weak itinerant magnetism is that the size of the ordered moment is significantly smaller than the size of the moment in the paramagnetic phase. 

Collaboration

• ​PHELIQS (UGA, CEA, Grenoble INP) 
• Paul Scherrer Insitute, Villigen, Switzerland 
• Babes-Bolyai University, Cluj-Napoca, Romania